Rotational and Circular Motion: MDCAT Notes and MCQs
Angular displacement
- Angle subtended at the centre by a body moving along a circle; θ = S/r. Vector along the axis (right-hand rule) for small angles.
- Radian: angle subtended at the centre by an arc equal to the radius.
- 1 revolution = 360° = 2π rad; 1 rad = 57.3°; 1° = 0.01745 rad.
Angular velocity & acceleration
- ω = Δθ/Δt (rad s−1); ω = 2πf = 2π/T. Direction along axis (right-hand rule).
- α = Δω/Δt (rad s−2).
Linear ↔ angular
| Linear | Relation |
|---|---|
| Displacement | S = rθ |
| Velocity | v = rω (v = r × ω) |
| Tangential acceleration | at = rα |
| Centripetal acceleration | ac = v²/r = rω² (towards centre) |
Equations of angular motion mirror linear ones: ωf = ωi + αt; θ = ωit + ½αt²; 2αθ = ωf² − ωi². Centripetal force Fc = mv²/r = mrω².
All points on a rotating rigid body have the same ω but different v — points farther from the axis move faster.
PMDC learning outcomes for this unit
- Angular quantities: 4.1 Define angular displacement, express angular displacement in radians.
- Angular quantities: 4.2 Define revolution, degree and radian
- Angular quantities: 4.3 Describe the term angular velocity
- Angular quantities: 4.4 Find the relationships between linear and angular variables, displacements, velocities and accelerations